how the eff do i teach myself trig in an hour

[melanie.dee]

i find myself just leaving these stupid questions entirely blank the whole time. i just do NOT get trig equations. like solving them with exact values and the unit circle and all that shit.

how do i teach myself this is an hour or less haha? anyone have any really simple explanations. i mean questions like

Find the exact solutions of cos(3xpi) = -sin(3xpi) for 0 < or equal to x < or equal to 1

and..

Solve the equation root(3)sin(2x) + cos(2x) = 0 for x is an element of [0,2pi], giving exact values in terms of pi.

I can normally work out how to get to part where i have something equal one of the things from the exact values thing, but then i dont know how many solutions i need and how to work them out or ANY of that shit.

[hifer]

i find myself just leaving these stupid questions entirely blank the whole time. i just do NOT get trig equations. like solving them with exact values and the unit circle and all that shit.

how do i teach myself this is an hour or less haha? anyone have any really simple explanations. i mean questions like

Find the exact solutions of cos(3xpi) = -sin(3xpi) for 0 < or equal to x < or equal to 1

and..

Solve the equation root(3)sin(2x) + cos(2x) = 0 for x is an element of [0,2pi], giving exact values in terms of pi.

I can normally work out how to get to part where i have something equal one of the things from the exact values thing, but then i dont know how many solutions i need and how to work them out or ANY of that shit.

In this type of questions, what u have to do is basically express the eqn using 1 trig function, eg for 1st qs:

cos(3xpi) = -sin(3xpi)   <- Divide both sides by cos(3xpi)
1 = -tan(3xpi)
tan(3xpi) = -1
Reference angle is pie/4 and angle is in 2nd and 4th quadrant
then proceed to solve for all solns in defined domain..

[kido_1]

These questions are easy...once you get the trick:

 1)sinx = cosx     is the same as (dividing both sides by cosx)
 tanx = 1

2) sin2x-cos2x=0
sin2x=cos2x
tan2x=1

3) cos100pix= sin100pix
tan100pix = 1

It gets boring after a while...
See if you can do your questions now. Just divide both sides by cos(angle).

[melanie.dee]

no no see thats the part i CAN do. i can transpose it and convert it to tan or whatever find. but i dont get how the whole reference angles thing works and quadrants and how to change the domain. actually i just did a prac question with the solutions next to me and that kinda helped i think i getit, but then normally i look at these questions and go wtf. actualy dw i dont think its anything i can get help with here haha. i think i need someone to explain to me in person. or ill try work it out haha.

[Fitness]

how do i teach myself this is an hour or less haha? anyone have any really simple explanations. i mean questions like

If you have some clue but forgot how and need to refresh your memory fast, the i suggest you try the reference note pads from the itute website.

Edit: Just realised that there is no specific trig notepad ... However some could be contained within others and these are still good for the other topics. Certainly got me on the right track with probability.

[costargh]

What are the 2 triangle thingos that you use to get your reference angles?
And when do you use them? haha

[reg]

You just need to get used to it.

We get to the stage:
tan(2x) = -sqrt(3).

tan(x) equals sqrt(3) at pi/3, and tan is negative in the 2nd and 4th quadrants  (ASTC).

Hence, we need pi-pi/3, 2pi-pi/3.

and we need solutions from 0 to 2pi .. (which is really 4pi because we have  tan(2x), so we change the domain)

pi - pi/3, 2pi - pi/3, 3pi - pi/3, 4pi - pi/3

so eventually we have:

2x = 2pi/3, 5pi/3, 8pi/3, 11pi/3
x = 2pi/6, 5pi/6, 8pi/6, 11pi/6

You just do pi-pi/3, 2pi-pi/3 until you consume all the required periods.

As far as exact values go, I just memorized the sin row, the cos row is sort of an inverse (easy to remember once you have sin down), and then tan is just division. I'll write out the table in the exam. But you should prolly go for the triangles

[Galelleo]

lol ... its hard to explain/draw the triangles on this... but here , i did it in paint  lol


[img]http://img207.imageshack.us/img207/5792/loldm4.th.jpg[/img]

[Fitness]

What are the 2 triangle thingos that you use to get your reference angles?
And when do you use them? haha

Ok well I too did a version of these triangles. See if you can follow this one easier ...

[Galelleo]

Basically, the triangels are from the smallest possible integers for the sides when you have the angels of 45, 60, and 30 on a right angld triangle.

lol if that makes sense...
the smallest sided equilateral triangle has sides of 1 but we use 2 beacuse we half it to find the angles easier... uh i just confused myself
basically when you cut them in half you get that picture, and theyre the values of sin (O/H), cos (A/H), and tan (O/A).

Alternatively, you can think about it for a moment and picture the general graph, you know cos starts at 1, when x=0... and you know the period is 2pi, so you just picture where on the graph, pi, pi on 2, pi on 4, pi on 3, pi on 6, would be and you can memories/guess the values of cos /sin/tan at that point... although its probably easier to have a calculater

[Galelleo]

sorry, im not explaining it very well

[melanie.dee]

Alternatively, you can think about it for a moment and picture the general graph, you know cos starts at 1, when x=0... and you know the period is 2pi, so you just picture where on the graph, pi, pi on 2, pi on 4, pi on 3, pi on 6, would be and you can memories/guess the values of cos /sin/tan at that point... although its probably easier to have a calculater

ahahah thats what i have to resort to doing hahaha. its just sliiightly time consuming lol. i think my problem is memorising the exact values. should i try to understand how the triangles work or should a did  lil bit o rote learning and memorise the values somehow. lol. god iv done NO eco study. im screwed for that now

[Fitness]

should i try to understand how the triangles work or should a did  lil bit o rote learning and memorise the values somehow. lol. god iv done NO eco study. im screwed for that now

Learn the triangles. Once you memorise them, you go from memorising like nine things to just a couple. They are easy if you try hard enough to remeber them.

[kingmar]

Try this one on for size. (I found it horrible, took me ages and timed my trial exam out)

Find exact solutions to the equation "1+sin(x) = 2(cos(x)squared) where x is in [0,2pi].

in words: one plus sine (x) equals two times (cos(x) squared).

[Fitness]

Try this one on for size. (I found it horrible, took me ages and timed my trial exam out)

Find exact solutions to the equation "1+sin(x) = 2(cos(x)squared) where x is in [0,2pi].

in words: one plus sine (x) equals two times (cos(x) squared).

What the hell? I just did it but am no way right .. lol

Answers?

Edit: Did it again and got x = pi/2, 3pi/2
Is this correct?